Using the TIME model in Spectrum to estimate tuberculosis–HIV incidence and mortality Carel Pretoriusa, Philippe Glazioub,M, Peter J. Doddc,M, Richard Whited,M and Rein Houbend Objectives: Reliable estimates of the joint burden of HIV and tuberculosis epidemics are crucial to planning strategic global and national tuberculosis responses. Prior to the Global Tuberculosis Report 2013, the Global Tuberculosis Programme (GTB) released estimates for tuberculosis–HIV incidence at the global level only. Neither GTB nor United Nations Programme on HIV/AIDS (UNAIDS) published country specific estimates for tuberculosis–HIV mortality. We used a regression approach that combined all available data from GTB and UNAIDS in order to estimate tuberculosis–HIV incidence and mortality at country level. Methods: A regression method was devised to relate CD4 dynamics (based on national Spectrum files) to an increased relative risk (RR) of tuberculosis disease. The objective function is based on least squares and incorporates all available country-level estimates of tuberculosis–HIV incidence. Global regression parameters, obtained from averaging results over countries with population survey estimates for tuberculosis– HIV burden, were applied to countries with no survey tuberculosis–HIV incidence estimates. Results: The method produced results that are in reasonably close agreement with existing GTB estimates for global tuberculosis–HIV burden. It estimated that tuberculosis–HIV accounts for 12.6% of global tuberculosis incidence, 21.3% of all tuberculosis deaths, and 20% of all HIV deaths as estimated by the Spectrum AIDS Impact Module (AIM). Regional estimates show the highest absolute incidence burden in East and Southeast Asia, and the highest per capita burden in sub-Saharan Africa, where between 12.5% (Central sub-Saharan Africa) and 60.6% (Southern sub-Saharan Africa) of all tuberculosis disease occurs in people living with HIV (PLWH). Tuberculosis mortality follows a similar pattern, except that a disproportionate percentage of global tuberculosis deaths (12.1%) relative to global incidence (8.7%) occurred in Southern sub-Saharan Africa. Conclusion: The disaggregation of tuberculosis incidence using a regression method on RR of tuberculosis disease and all available data on HIV burden (from UNAIDS) and tuberculosis–HIV testing (survey, sentinel and routine surveillance data) produces results that closely match GTB estimates for 2011. The tuberculosis–HIV incidence and mortality results were published in the Global Tuberculosis Report 2013. Several limitations of and potential improvements to the process are suggested. ß 2014 Wolters Kluwer Health | Lippincott Williams & Wilkins
AIDS 2014, 28 (Suppl 4):S477–S487 Keywords: estimates, HIV, regression model, tuberculosis
a Futures Institute, Glastonbury, Connecticut, 06033, USA, bGlobal TB Programme, World Health Organization, 20 avenue Appia, 1211 Geneva 27, Switzerland, cHealth Economics and Decision Science, School of Health and Related Research, University of Sheffield, Sheffield, S1 4DA, UK, and dTB Modelling Group, TB Centre, London School of Hygiene and Tropical Medicine, UK. Correspondence to Carel Pretorius, Futures Institute, Glastonbury, CT, 06033, USA. E-mail:
[email protected] Philippe Glaziou, Peter J. Dodd and Richard White contributed equally to the writing of this article. Received: 9 September 2014; revised: 9 September 2014; accepted: 9 September 2014.
DOI:10.1097/QAD.0000000000000484 ISSN 0269-9370 Q 2014 Wolters Kluwer Health | Lippincott Williams & Wilkins. This is an open-access article distributed under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License, where it is permissible to download and share the work provided it is properly cited. The work cannot be changed in any way or used commercially.
S477
S478
AIDS
2014, Vol 28 (Suppl 4)
Introduction HIV and tuberculosis remain two of the most challenging global public health problems for national and global planners alike. According to the Global Tuberculosis Report 2013 [1], 8.6 million people developed tuberculosis in 2012. Among these cases, 1.3 million died from tuberculosis disease, including 320 000 tuberculosis–HIV associated deaths. Targets for the reduction in tuberculosis deaths are clearly set out in WHO declarations such as the Millennium Development Goals (MDGs). Significant progress has been made in fighting tuberculosis and tuberculosis–HIV through following the WHO strategies for these diseases. Tuberculosis incidence and tuberculosis-associated mortality is now on a continuing downward trend, but more can be done to accelerate progress towards achieving MDG impact targets, which aim to halve the 1990 number of HIV/tuberculosis deaths by 2015. Global health partners, including the WHO and the Global Fund to Fight AIDS, Tuberculosis and Malaria, are committed to setting further targets and monitoring progress in fighting HIV, tuberculosis and joint tuberculosis–HIV epidemics. As part of these efforts, countries need tuberculosis–HIV-related estimates for both planning and monitoring purposes. For example, 41 high-burden countries are now required to submit joint tuberculosis/ HIV ‘concept notes’ or applications to the Global Fund to Fight AIDS, tuberculosis and Malaria as mandated in their new funding model [2]. Estimates of tuberculosis–HIV mortality at the country level have been produced by Global Tuberculosis Programme (GTB), relying partly on overall HIV prevalence estimates from UNAIDS. Recent changes to the Spectrum AIDS Impact Module (AIM) model structure present a more detailed picture of HIV burden. Tuberculosis–HIV estimates are also accumulating through population surveys of tuberculosis–HIV prevalence, sentinel HIV data, and routine HIV testing of reported tuberculosis cases. These recent changes prompted an initiative to produce improved tuberculosis–HIV mortality estimates at the national level. A collaboration between GTB, UNAIDS, TB Modelling and Analysis Consortium (TB MAC), the Stop TB Partnership, Futures Institute, and a wide group of experts was launched under the auspices of the UNAIDS Reference Group on Estimates, Modelling and Projections. The aim was to assess all available data and methods for combining data sources from GTB and UNAIDS in order to produce the best estimates for tuberculosis–HIV burden. A method was developed by Futures Institute and finalized by the reference group. This study offers a technical account of this method, which has been integrated into TIME (TB Impact Model and Estimates)
[3], a wider suite of tuberculosis tools in Spectrum [4,5], under the name TIME Estimates. TIME Estimates uses a regression model that relates the seven CD4 categories of the adult HIV population in Spectrum AIM to their relative risk (RR) for tuberculosis disease. The model does not attempt to simulate any parts of tuberculosis natural history or care and control in a mechanistic way, but looks to directly distribute the overall burden of incident tuberculosis across HIV/CD4 strata. The model draws no distinction between adult and pediatric tuberculosis, and assumes that combined adult and childhood tuberculosis can be regressed on adult HIV CD4 distributions. To this end, a regression method for tuberculosis incidence was devised to estimate RR for tuberculosis incidence. The model was fit to total estimated incidence from the WHO GTB database [6] and disaggregated according to HIV burden numbers, which were further disaggregated by the seven CD4 categories used by Spectrum AIM for national HIV projections. Tuberculosis mortality was calculated as the product of number of incident cases and estimated case fatality ratios (CFRs) by HIV/antiretroviral therapy (ART) and tuberculosis notification status.
Methods Methods are presented in five sections: (1) A brief overview of the cubic-spline method used in the analysis, (2) a bootstrap method for obtaining confidence intervals, (3) functional form for the regression method to estimating tuberculosis–HIV incidence, (4) the objective function used, and (5) the use of CFRs to estimate tuberculosis–HIV mortality.
Projection with cubic splines The regression methods used by TIME relied on estimation with cubic-splines (penalized B-splines in particular), a technique widely used use for projecting trends forward in time. The same method was used as one of the techniques of shaping the force of infection of HIV in the Estimation and Projection Package (EPP) estimation approach [7]. In simple terms, this can be explained as follows: A time-dependent function, such as tuberculosis incidence, which is called I(x) below, can be represented as a linear combination of cubic-spline basis functions. Keeping the specification general, the linear representation involves k time-dependent m’th order cubic-spline functions [8]: X IðxÞ ¼ bi Bm iðxÞ (1) i¼1 to k
Using the TIME model in Spectrum to estimate tuberculosis–HIV incidence and mortality Pretorius et al.
where bi is the i’th spline coefficient and Bmi(x) represents the evaluation of the i-th basis function at time(year) x. We used 10 equally spaced knots (k ¼ 10), which sufficiently span the projection period of 1990–2012. The order of each basis function was m, and we used cubic-splines, that is, m ¼ 3, as in EPP. For our application, the values of the cubic-spline coefficients b were determined by an optimization routine that minimized the least squares error between incidence data (Iobs) and the estimated curve I(x): X jIðXÞ Iobs ðXÞj2 þ lbT Sb (2) x¼1990:2012
Here jI - Iobsj2 is the sum of squared errors, S a secondorder difference matrix, and l a smoothness penalty matrix applied directly to the parameters b to control the level of variation between adjacent coefficients of the cubic-spline.
Global Tuberculosis Programme data The most successful approach to estimating tuberculosis incidence at national level is through routine surveillance systems, on which reports of notified new and relapse cases are based. Generally, countries with universal health coverage have near complete notification reports, providing a reliable proxy for tuberculosis incidence [9]. However, surveillance system often fail to provide a reliable estimate of tuberculosis incidence, the major reasons of which include: laboratory errors [10], lack of notification by public [11] and private providers [12], failure of health-care staff to recognize tuberculosis signs and symptoms among people accessing health services [13] and lack of access to health services [14]. These factors all contribute to uncertainty about tuberculosis incidence estimates obtained from case notification data. Reliance on expert opinion to estimate incidence in countries with weak surveillance and health systems often result in biases in estimates and considerable uncertainty in tuberculosis estimates, as mentioned in the Global Tuberculosis Report [1].
The prevalence of HIV among reported new and relapse tuberculosis cases is used as a proxy for HIV prevalence among incident tuberculosis. Sources of data at country level include nationwide representative HIV serological surveys among a sample of reported tuberculosis cases, data from HIV sentinel groups, and results from routine testing of tuberculosis patients when testing coverage of newly reported cases is high.
Tuberculosis indicators and fitting algorithm The cubic-spline projection method outlined above was adapted to fit and project a number of tuberculosis indicators relevant to this analysis. A general framework was used to control the terms that define each objective function, which comprise terms that minimize the error in fitting to data and terms that ensure smoothness of the fit. The method available in Spectrum TIME was replicated in MATLAB to facilitate batch processing, using the fmincon function with its Levenberg–Marquardt minimization method for non-linear least squares problems [15]. This analysis required projections for total tuberculosis notification and incidence, the ratio of which determined the case detection ratio (used in tuberculosis mortality calculations), as well as the breakdown of total tuberculosis incidence into HIV status. These indicators are described in Table 1. Overall tuberculosis incidence and notification were first estimated directly from respective data. The projected tuberculosis incidence figures were then used as simulated data, together with observed tuberculosis–HIV data, to estimate disaggregations into three assumed tuberculosis incidence components: HIV-negative, HIV-positive not on ART, and HIV-positive on ART tuberculosis cases (see section ‘Tuberculosis–HIV incidence disaggregation’). Tuberculosis mortality was finally determined using incidence and notification projections, in order to apply different case fatality ratios to incident and notified tuberculosis cases (see section ‘Estimating Tuberculosis– HIV mortality’). For tuberculosis indicators directly fitted to data (total tuberculosis notification and incidence), we used
Table 1. Indicators fitted with cubic splines, either directly or through functional relationship. Regressand
Regressor
Description and/or purpose
Direct fitting Total tuberculosis incidence (I)
Spline coefficients b
Provides envelope for HIV-negative and HIV-positive tuberculosis incidence Determines case detection ratio ¼ N/I, used in mortality calculations
Total tuberculosis notification (N) Fitting through composite functional relationship Total tuberculosis incidence, tuberculosis–HIV survey, sentinel and routine survey data
Spline coefficients b Spline coefficients b Tuberculosis–HIV progression parameter
Provides estimate for risk of tuberculosis infection for HIV-negative and CD4þ cell count > 500 cells/ml tuberculosis cases Provides fit to available tuberculosis–HIV data
S479
S480
AIDS
2014, Vol 28 (Suppl 4)
generalized cross-validation [8] to determine a smoothness parameter. We did not apply a smoothness penalty to estimate the breakdown of projected total tuberculosis incidence by HIV status.
Confidence intervals The cubic-spline method was then used to fit an indicator (incidence or notification) to a set of bootstrapped data, obtained by sampling from the normal error distribution with zero mean and a standard deviation of the residuals of the spline regression. This bootstrap method produced a sample of projected cubic-spline curves that inherits the temporal biases and systematic errors of the data. Confidence intervals based on the bootstrapped data, namely 2.5th and 97.5th percentile of projected cubic splines, were typically narrow in the years where the model had data to utilize, and ‘spread out’ after that, according to a Gaussian process with a linearly increasing variance. Note our confidence intervals do not propagate the uncertainty bounds around tuberculosis incidence described in the GTB datasets, but rather represent uncertainty arising from our spline fit to the GTB bestestimate time series.
Tuberculosis–HIV incidence disaggregation The disaggregation of tuberculosis incidence by HIV and CD4 category is based on the idea that increase in the RR for tuberculosis incidence is a function of CD4 decline. Williams et al. [16] captured this idea in a model for the relationship between the RR for tuberculosis and CD4 decline. They suggested a 42% (26–59% for the 95% confidence interval) increase in RR for tuberculosis for each unit of 100 ml CD4 decline. The model approximated this principle by first estimating HIVnegative tuberculosis incidence, and then calculating the ‘risk of tuberculosis’ function F(HIV-negative) ¼ I / P, where I is HIV-negative tuberculosis incidence and P the number of HIV-negative individuals susceptible to tuberculosis.
CD4 category relative to 500: dc ¼ (0, 0.8, 2.0, 2.8, 3.6, 4.3, 4.8) for the seven CD4 categories. There are a number of aspects of the RR approach that have to be balanced: the ‘biological meaning’ we would like to attach to these parameters, and a more straightforward interpretation of these parameters as regression coefficients. Either or both parameters can be fixed or allowed to vary to fit the data. For the 2012 estimates, we assumed p(1) ¼ 2.5 [17] and fit p(2) in order to match total tuberculosis incidence and tuberculosis– HIV estimates from HIV-test data where available. We further assumed hazard ratios of 0.35 for all CD4 at ART initiation categories. Suthar et al. [18] reports hazard ratios of 0.16, 0.35, and 0.43 for those on ART with CD4þ cell count less than 200, 200–350, and more than 350 cells/ml, and these values could in principle be used. However, we used a single hazard ratio corresponding to the prevailing CD4-based eligibility criterion at 2012. A further assumption was made that the hazard ratio of 0.35 applied only to patients on ART for more than 6 months. Spectrum’s ART-mortality estimates, derived mostly from ART cohorts in Southern sub-Saharan Africa, suggested that mortality is still very high in the first 6 months of treatment. As tuberculosis is a leading cause of HIV mortality, it was felt that the hazard ratio of 0–6 month ART patients is likely still high and the reduction factor due to ART was not applied. The above algorithm can be described by a general formula for incidence I: X Ih ðtÞ ¼ Ph;c FðtÞ Ah;c Bh;c c
(3)
Where h is a label for HIV status: HIV-negative (h ¼ 1), HIV-positive not on ART (h ¼ 2), and HIV-positive tuberculosis cases on ART for 0–6 months (h ¼ 3), 7–12 months (h ¼ 4), and more than 1 year (h ¼ 5), and c a label for the seven CD4 categories of each HIV-positive state (h 2). Ph,cis the population size of group h, c (when h ¼ 1, c does not apply). Ah,c ¼ p(1) p(2)dc for h2 or more and c ¼ 1–7 (1 otherwise) and Bh,c ¼ 0.35 for h4 or more (1 otherwise). The cubic spline parameters for the ‘risk of tuberculosis’ function F(t) as well as p(2) is estimated in an optimization step so as to minimize the sum of squared residuals between predicted tuberculosis– P HIV incidence ( h>¼2Ih), described in the next section, as well as a simulatedP(bootstrap) dataset for overall tuberculosis incidence ( h>¼1 Ih).
where p(1) is a parameter that was used to recognize that PLWH, even with high CD4þ cell counts, are at higher risk of tuberculosis relative to HIV-negative cases, and p(2) controls the exponential increase in RR with CD4 decline. The CD4 decline unit dc is the number of 100 mL CD4 decline associated with the midpoint of each
Objective function for tuberculosis–HIV estimates A simple least squares approach was used to fit the model to total tuberculosis incidence and to all available estimates of tuberculosis–HIV incidence. Weighting of the data on HIV-positive tuberculosis incidence was
An assumption was made that the risk of tuberculosis for PLWH cases with CD4þ cell count more than 500 ml was proportional to F(HIV-negative). For each 100 ml CD4 decline in the remaining categories (350–499, 250–349, 200–249, 100–199, 50–99 CD4þ cells/ml, and CD4þ cell count less than 50 cells/ml), the risk of tuberculosis as a function of CD4þ cell count was represented as: Fðc < 500Þ ¼ FðHIV-negativeÞ pð1Þ pð2Þdc ;
Using the TIME model in Spectrum to estimate tuberculosis–HIV incidence and mortality Pretorius et al.
dependent on the perceived strength of the data point. Estimates of HIV-positive tuberculosis incidence were obtained by three sampling methods: population surveys of tuberculosis–HIV prevalence (least biased, but scarce due to cost), sentinel HIV data (biases included more testing of advanced HIVespecially in resource constrained settings), and routine HIV testing of reported active cases (variable coverage as is characteristic of different contexts). To increase the weight of survey data, we duplicated the survey data in the objective function for years with HIVtest data, we simply added identical copies of the HIV-test data to the objective function. This is a way of (subjectively) giving more weight to HIV-test data in the objective function, in which function it would be competing with our total tuberculosis incidence estimate. The total tuberculosis incidence estimate was based on much more data, evenly spread out in the estimation period 1990–2015. Our method makes no correction for the degree to which tuberculosis–HIV prevalence fails to approximate tuberculosis–HIV incidence, a point elaborated upon in the concluding section. Trial and error showed that using two replicas of the HIV survey data (i.e., duplicating the survey data) HIV sentinel data with coverage greater than 90%, and routine testing estimates with coverage between 50–90% (routine testing data with coverage 0–50% are not used), gives a fit that passes close to survey points where they are available. For countries with no data, we used a range for p(2) based on results from countries with survey data, which suggested that p(2) ¼ 1.96 (1.8–2.1) and fit the RR model only to total tuberculosis incidence. We imposed a lower bound of 1.3 and an upper bound of 3.7 on p(2) when fitted to countries with survey data. There is no satisfactory way of verifying results for HIV-positive tuberculosis incidence when no HIV-testing data are available, but comparison of the global estimate for HIVpositive tuberculosis incidence produced by Spectrum tuberculosis and GTB’s estimate (based a different method using HIV prevalence instead of CD4 distributions and using the same HIV-test but in a different way) suggested that the RR model worked reasonably well.
Estimating tuberculosis–HIV mortality Tuberculosis mortality is affected by a complex relationship between active tuberculosis disease and many clinical variables, which we approximated in a simple functional relationship between incidence and CFR. For the purpose of this work, CFR was defined as the ‘fraction of individuals with active tuberculosis that will die due to tuberculosis, during that tuberculosis episode, regardless of the duration of that episode.’ This follows the definition used by Straetemans et al. [19] and included deaths recorded as ‘with tuberculosis as contributory
cause’, ‘attributable to tuberculosis’ or ‘related to tuberculosis’. We considered eight categories CFRs (HIV negative, HIV positive not on ART, HIV positive on ART
